Layered phase field approach to shells

Fracture is one of the most commonly encountered failure modes of engineering materials and structures. Prevention of cracking-induced failure is, therefore, essential to save lives and contain costs and should be considered a social commitment. However, the understanding of nucleation and propagation of complex crack patterns in real structures is still an open problem, for which traditional techniques are unable to provide satisfactory results. In this field, the variational formulation of fracture mechanics as an energy minimisation problem opened new perspectives; in particular, the phase field approach to fracture revealed to be a versatile and powerful tool for the investigation of crack problems. Despite the widespread use of plates and shells in engineering applications, the failure mechanisms of these kind of structures are quite poorly understood. As a matter of fact, few attempts have been devoted to the formulation and applications of the phase field approach to plates and shells. In this contribution an alternative phase field formulation is proposed, which relies on the subdivision of the thin (or slender) solid into several layers. In this way, while the mechanical behaviour of the solid is governed by classical theories of plates and shells, the phase field equation has to be satisfied within each layer, that is, in a domain with reduced dimension. The proposed procedure is validated and critically examined.